Math-o-semantics

I just visited a web site devoted to math challenges for children. I came across it while I was searching for a book that might offer interesting challenges for our granddaughter. It's called "Aunty Math" and says it's appropriate for children in Kindergarten through 5th grade.

This is today's problem posed at the site:
Which of the following numbers does not belong with the rest, and why? 1, 3, 4, 9, 25.

Do you know the answer? Are you sure? This is math, remember, not some touchy-feely psycho-babble pseudo-science course. Or is it?

After I looked at the problem and decided on my answer, I followed the link to, "Notes to Teachers and Parents". Here's what I found: There is no one correct answer. This is an "open-ended" problem.

According to the author, instead of one correct answer, parents and teachers should instead look for:

• - Fluency - How many solutions can the student create?
• - Flexibility - How many math ideas can the student discover?
• - Originality - To what extent is the student's idea original?
• - Elegance - To what degree is the student's expression of the idea simple and clear?

At the bottom of the page it says: "Sometimes students (and teachers and parents) are resistant to the idea that there can be multiple solutions to math problems. However, in today's world, this is very often the case. Teaching children mathematics through "open-ended" problems helps prepare them for the math they will encounter in the 21st century."

This sounds an awful lot like what I heard back in the '80s: "It doesn't matter that Johnny can't spell as long as he expresses himself creatively."

Count me among those who are resistant the idea of blurry math solutions before children have firmly established math foundations.